Graphing Linear Equations 6.7 Graphing Linear Equations

Rectangular Coordinate System The horizontal line is called the x-axis. The vertical line is called the y-axis. The point of intersection is the origin. x-axis y-axis origin Quadrant I Quadrant II Quadrant III Quadrant IV

Plotting Points Each point in the xy-plane corresponds to a unique ordered pair (a, b). Plot the point (2, 4). Move 2 units right Move 4 units up 2 units 4 units

Determine if the ordered pair satisfies the equation 3x – 2y = 10 (-1 , 4) 3(-1) – 2(4) = 10 -3 – 8 ≠ 10 Therefore, (-1, 4) is not a solution

To Graph Equations by Plotting Points Solve the equation for y. Select at least three values for x and find their corresponding values of y. Plot the points. The points should be in a straight line. Draw a line through the set of points and place arrow tips at both ends of the line.

Graphing Linear Equations Graph the equation y = 5x + 2 3 1 2/5 2 y x

Graphing Using Intercepts The x-intercept is found by letting y = 0 and solving for x. Example: y = 3x + 6 0 = 3x + 6 6 = 3x 2 = x The y-intercept is found by letting x = 0 and solving for y. Example: y = 3x + 6 y = 3(0) + 6 y = 6

Example: Graph 3x + 2y = 6 using the x- and y-intercepts Find the x-intercept. 3x + 2y = 6 3x + 2(0) = 6 3x = 6 x = 2 Find the y-intercept. 3(0) + 2y = 6 2y = 6 y = 3

Practice Problem: graph using either method

Slope The ratio of the vertical change to the horizontal change for any two points on the line. Slope Formula:

Types of Slope Positive slope rises from left to right. Negative slope falls from left to right. The slope of a vertical line is undefined. The slope of a horizontal line is zero. zero negative undefined positive

Example: Finding Slope Find the slope of the line through the points (5, 3) and (2, 3).

Practice Problem: Find the slope given the two points (-3, 2) and (1, 5)

The Slope-Intercept Form of a Line Slope-Intercept Form of the Equation of the Line y = mx + b where m is the slope of the line and (0, b) is the y-intercept of the line.

Graphing Equations by Using the Slope and y-Intercept Solve the equation for y to place the equation in slope-intercept form. Determine the slope and y-intercept from the equation. Plot the y-intercept. Obtain a second point using the slope. Draw a straight line through the points.

Example Graph 2x  3y = 9. Write in slope-intercept form. The y-intercept is (0,3) and the slope is 2/3.

Example continued Plot a point at (0,3) on the y-axis. Then move up 2 units and to the right 3 units.

Practice Problem: state the slope and y-intercept. Then graph

Horizontal Lines Graph y = 3. y is always equal to 3, the value of y can never be 0. The graph is parallel to the x-axis.

Vertical Lines Graph x = 3. x always equals 3, the value of x can never be 0. The graph is parallel to the y-axis.

Practice Problem: Graph the following

Homework P. 345 # 9 – 90 (x3) # 9 -24 can be on one axes